相关论文: Piecewise Extended Chebyshev Spaces: a numerical t…
In this paper, we provide a statistical testing framework to check whether a random sample splitting in a multi-dimensional space is carried out in a valid way, which could be directly applied to A/B testing and multivariate testing to…
For an arbitrary given span of high-dimensional multivariate Chebyshev polynomials, an approach to construct spatial discretizations is presented, i.e., the construction of a sampling set that allows for the unique reconstruction of each…
We study the completeness and ultracompleteness numbers of a convergence space. In the case of a completely regular topological space, the completeness number is countable if and only if the space is $\v{C}$ech-complete, and the…
The equivalent permeability of a randomly cracked porous material is studied using a finite element program in which a four-nodes zero-thickness element is implemented for modelling the cracks. The numerical simulations are performed for…
These lecture notes contain an extended version of the material presented in the C.I.M.E. summer course in 2017, aiming to give a detailed introduction to the metric Sobolev theory. The notes are divided in four main parts. The first one is…
We study the periods mapping from the moduli space of real hyperelliptic curves with marked point on an oriented oval to the euclidean space. The mapping arises in the analysis of Chebyshev construction used in the constrained optimization…
Let $X$ be a zero-dimensional space and $C_c(X)$ be the set of all continuous real valued functions on $X$ with countable image. In this article we denote by $C_c^K(X)$ (resp., $C_{c}^{\psi}(X)$) the set of all functions in $C_c(X)$ with…
Graphical (Linear) Algebra is a family of diagrammatic languages allowing to reason about different kinds of subsets of vector spaces compositionally. It has been used to model various application domains, from signal-flow graphs to Petri…
In a separably connected space any two points are contained in a separable connected subset. We show a mechanism that takes a connected bounded metric space and produces a complete connected metric space whose separablewise components form…
We show how to decompose all separable ultrametric spaces into a "Lego" combinations of scaled versions of full simplices. To do this we introduce metric resolutions of large scale metric spaces, which describe how a space can be broken up…
A \emph{complete geometric graph} consists of a set $P$ of $n$ points in the plane, in general position, and all segments (edges) connecting them. It is a well known question of Bose, Hurtado, Rivera-Campo, and Wood, whether there exists a…
Generalization, i.e., the ability of solving problem instances that are not available during the system design and development phase, is a critical goal for intelligent systems. A typical way to achieve good generalization is to learn a…
New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…
A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature,…
Piecewise Translations is a class of dynamical systems which arises from some applications in computer science, machine learning, and electrical engineering. In dimension 1 it can also be viewed as a non-invertible generalization of…
Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility $\leq_c$. This gives rise to a rich degree-structure. In this…
An infinite dimensional notion of asymptotic structure is considered. This notion is developed in terms of trees and branches on Banach spaces. Every countably infinite countably branching tree $\mathcal T$ of a certain type on a space X is…
We consider $\ell_p$-direct sums ($1\leq p<\infty$) and $c_0$-direct sums of countably many normed spaces and find the duals of these spaces. We characterize the support functionals of arbitrary elements in these spaces to characterize…
} The main goal of this note is to provide new, mostly multidimensional densities, compactly supported and list many of its properties that enable effective calculations. The idea of obtaining such densities is firstly to build some…
Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigenvectors of the graph Laplacian. One attractive application of ER is to point clouds, i.e. graphs whose…